A lens system is said to be "color-corrected" for a specified number of wavelengths, if paraxial marginal rays passing through the system are brought to a common focus on the optic axis of the system for that specified number of wavelengths. Axial chromatic aberration in the lens system is zero at the wavelengths for which "color correction" is achieved, i.e., at the wavelengths for which paraxial marginal rays are brought to the common focus.
A lens system that has zero axial chromatic aberration at two wavelengths is said to be color-corrected for those two wavelengths, and is called an "achromatic" system. A lens system that has zero axial chromatic aberration at three wavelengths is said to be color-corrected for those three wavelengths, and is called an "apochromatic" system. It is customary to speak of a "three-color" system, or a "four-color" system, or a "five-color" system, etc., when referring to a lens system that is color-corrected for three wavelengths, or four wavelengths, or five wavelengths, etc.
A lens system that is color-corrected for a specified number of wavelengths can be designed using a desired number of different kinds of optical materials (even as few as only two different kinds of optical materials) for the lens elements comprising the system, provided that the dispersion properties of the different kinds of optical materials selected for the lens elements of the system are related to each other. In such a way that zero axial chromatic aberration in the system is possible at the specified number of wavelengths. If the optical materials selected for the lens elements of the system are inherently compatible with each other so as to make color correction of the system possible at the specified number of wavelengths, the lens designer must still optimize geometrical parameters (e.g., thicknesses, radii of curvature, spacings) of the lens elements in order to develop a design form (i.e., an "optical prescription") for the system that actually results in color correction at the specified number of wavelengths. However, unless compatible optical materials are selected ab initio for the lens elements of the system, no amount of effort by the designer in attempting to optimize the geometrical parameters can result in color correction of the system at the specified number of wavelengths.
The selection of compatible optical materials is a necessary condition for designing a lens system that is to be color-corrected at a desired number of wavelengths. However, it is not sufficient merely to select compatible optical materials in order to design a color-corrected lens system. The lens designer, having first selected compatible optical materials, must then develop a design form using the selected optical materials for the lens elements of the system. In general, even if compatible optical materials are used, the development of a design form for a lens system that is to be color-corrected at three or more wavelengths requires considerable creative skill. The design form for a color-corrected lens system can be of patentable merit in its own right, even if the designer knows beforehand of one or more possible combinations of optical materials that could be used for the lens elements of the system in order to achieve color correction at the desired number of wavelengths.
A technique was disclosed in co-pending U.S. patent application Ser. No. 419,705, filed on Sept. 20, 1982, for selecting compatible optical materials for use in designing an optical system that is to be color-corrected at a specified number of wavelengths. This technique involves expressing the index of refraction of each optical material available to the designer in a power series expression derived from Buchdahl's dispersion equation, and then comparing corresponding coefficients in the power series expressions for the different optical materials. In designing an optical system that is to be color-corrected at three wavelengths using only two different optical materials for the refractive elements of the system, only those optical materials can be used for which the ratios of corresponding coefficients are equal in the quadratic form of the power series expressions for their refractive indices. Similarly, only those pairs of optical materials for which the ratios of corresponding coefficients are equal in the cubic form of the power series expressions for their refractive indices can be used for the refractive elements of an optical system made of two different optical materials that is to be color-corrected at four wavelengths. Likewise, only those pairs of optical materials for which the ratios of corresponding coefficients are equal in the quartic form of the power series expressions for their refractive indices can be used for the refractive elements of an optical system made of two different optical materials that is to be color-corrected at five wavelengths.
It was shown by R. I. Mercado in an article entitled "The Design of Apochromatic Optical Systems", SPIE, Vol. 554, (1985), pages 217-227, that power series expressions for the refractive indices of optical materials can be derived from various other well-known dispersion equations, including those of Hartmann, Cauchy, Schmidt and Conrady. In general, regardless of how the power series expressions for the refractive indices are derived, a necessary condition for obtaining color correction of an optical system at a desired number of wavelengths using two different optical materials for the refractive elements of the system is that the ratios of corresponding coefficients in the power series expressions for the refractive indices of the two different optical materials selected by the designer must be substantially equal to each other for a specified number of terms in the power series expressions, where the specified number of terms for which the ratios of corresponding coefficients must be equal to each other is one less than the number of wavelengths for which color correction of the system is desired.
It was further shown by R. D. Sigler in an article entitled "Glass Selection for Airspaced Apochromats Using the Buchdahl Dispersion Equation", Applied Optics, Vol. 25, No. 23, (1986), pages 4311-4320, that the necessary condition for achieving color correction of an optical system at three wavelengths using three (or more) different optical materials for the refractive elements of the system involves a relationship between corresponding coefficients in the power series expressions for the refractive indices of the selected optical materials that is less restricted than the relationship required between corresponding coefficients in the power series expressions for the refractive indices of a selected pair of optical materials when only two different optical materials are used for the refractive elements of the system.
The coefficients in a power series expression for the index of refraction of any particular optical material at any particular wavelength in a wavelength range of interest to the designer can be determined by fitting measured values for the index of refraction (which are usually supplied by the manufacturer of the optical material) at certain specified wavelengths (usually specified Fraunhofer lines) to a curve extending throughout the wavelength range of interest. A discussion of how the coefficients in power series expressions for indices of refraction derived from Buchdahl's dispersion equation were determined for certain optical glasses was provided by P. N. Robb et al. in an article entitled "Calculations of Refractive Indices Using Buchdahl's Chromatic Coordinates", Applied Optics, Vol. 22, No. 8, (1983), pages 1198-1215.
Coefficients in power series expressions for the refractive indices of commercially available optical glasses at specified wavelengths can be determined with more or less accuracy, depending upon the accuracy of measured values for refractive indices supplied by the manufacturers of the optical glasses, and upon the conformity of individual batches of the glass of each type to the particular melt of the glass of that type for which the measured values of refractive indices were obtained by the manufacturer. With regard to crystals, measured values for refractive indices at various wavelengths for certain optically useful crystals have been reported in the literature, and therefore the coefficients in power series expressions for the refractive indices of such crystals can be determined with more or less accuracy depending upon the extent to which measured refractive index data are available. It is to be noted, however, that measured refractive index data for crystals are not as plentiful (and generally are not as accurate) as measured refractive index data for optical glasses. With regard to optically useful plastic materials, measured refractive index data sufficiently accurate to enable coefficients of higher-order terms in power series expressions for refractive indices to be determined by curve fitting techniques are presently available for only a few different kinds of plastic materials.
In a power series expression for the index of refraction of an optical material based upon Buchdahl's dispersion equation, the coefficient of the first term is called the primary dispersion coefficient and the coefficient of the second term is called the secondary dispersion coefficient. If the primary dispersion coefficients for all the optical materials of interest to the optical designer are plotted against the secondary dispersion coefficients for the same optical materials in a rectangular Cartesian coordinate system, a graphical distribution of points is obtained in which each point represents a corresponding optical material. This type of plot is called a Buchdahl dispersion plot, which is analogous to the well-known Herzberger partial dispersion plot in which Abbe numbers are plotted against values of partial dispersion for the optical materials of interest to the optical designer.
In the Herzberger partial dispersion plot, the distribution of points representing the optical materials of interest are clustered about a straight line called the "normal line". Those materials represented by points that lie relatively close to the normal line on the Herzberger partial dispersion plot are said to have "normal" dispersion, and those materials represented by points that lie relatively far away from the normal line are said to have "abnormal" dispersion. A mathematical correlation can be shown to exist between the Herzberger partial dispersion plot and the Buchdahl dispersion plot. Thus, in a Buchdahl dispersion plot for optical glasses, a straight line called the "normal line for glasses" can be drawn that is analogous to the "normal line" of a Herzberger partial distribution plot. Conventionally, the normal line of a Herzberger partial dispersion plot is a straight line formed by a least-squares fit through all the plotted points. However, the normal line for glasses on a Buchdahl dispersion plot for optical glasses is a straight line formed by connecting the points representing two readily available glasses known to have normal dispersion, viz., Schott BK7 glass and Schott F2 glass.
The "normal line for glasses" formed on a Buchdahl dispersion plot for optical glasses can be superimposed onto a Buchdahl dispersion plot for other optical materials. By analogy to the Herzberger partial dispersion plot, those materials represented by points that lie relatively close to the normal line for glasses on the Buchdahl dispersion plot can be said to have "normal" dispersion, and those materials represented by points that lie relatively far away from the normal line for glasses on the Buchdahl dispersion plot can be said to have "abnormal" dispersion. As has long been realized by optical designers, it is necessary in designing a lens system that is to be color-corrected at three wavelengths for at least one lens element of the system to be made of an optical material having abnormal dispersion.
Fluidal liquids have been employed for optical purposes since antiquity. As used herein, the term "fluidal liquid" refers to a liquid in the commonly understood sense of the word, i.e., a liquid-phase material that flows to assume the shape of its container. Thus, a fluidal liquid is distinguished from a "glass", which (although technically a liquid) is a rigid (i.e., non-fluidal) optical material. It is a well-known expedient in optical engineering to use a fluidal liquid as a coupling medium between rigid lens elements for "index matching", i.e., to reduce the discontinuity between the refractive indices of consecutive lens elements. Fluidal liquids have also been used for thermal control in optical applications, and as lasing media in dye lasers. However, until the present invention, there had been no realization by optical designers that fluidal liquids can be selected for use as lens elements for the purpose of providing color correction at three or more wavelengths. The use of fluidal liquid lens elements in designing three-color lens systems had not been considered as a practical possibility in the prior art, because lens designers were generally unaware that many fluidal liquids have abnormal dispersion properties.
Published data on measured values of refractive indices for fluidal liquids have generally been inadequate for determining the coefficients of higher-order terms in power series expressions for the refractive indices of optically useful fluidal liquids. Consequently, fluidal liquids have been ignored by optical designers as candidate optical materials for use in designing color-corrected optical systems. There had been no incentive in the prior art to investigate the possibility of using fluidal liquids for the purpose of designing color-corrected optical systems, because the fact that many fluidal liquids are abnormally dispersive was generally unappreciated in the prior art.
It was known in the prior art that, for most fluidal liquids, the refractive index at a specified wavelength varies to a considerable extent with temperature. Therefore, in the absence of an awareness that many fluidal liquids have abnormal dispersion properties, there was no inducement in the prior art for optical designers to investigate the practicability of using fluidal liquids (which have the disadvantage of being temperature-sensitive) in place of optical glasses (which have the advantage of being temperature-stable) for the refractive elements of optical systems not specifically requiring fluidal liquids for mechanical or thermodynamic reasons.